Live practice

Proceed from the given expression and keep every transformation explicit.

The last line satisfies the required domain and establishes the result.

No. The same first coordinate may arise from different factor pairs with different sums. For example, \((a,b)=(0,0)\) gives the ordered pair \((0,0)\), while \((0,1)\) gives \((0,1)\). Thus input 0 has two images.

Every mole of BaSO₄ contains one mole of sulfur. Use the sulfur mass fraction in the precipitate.

A conjugate acid-base pair differs by one proton. Remove H⁺ from an acid to obtain its conjugate base, or add H⁺ to a base to obtain its conjugate acid.

Be₂ has equal numbers of electrons in σ2s and σ*2s after the core orbitals cancel. Its bond order is zero, so no net bond results.

Electronic energy and size depend on charge, shell number and shielding. Nuclear mass has negligible effect on valence electronic chemistry.

Convert both lengths to metres and divide the total length by one atomic diameter.

Calculate the moles of HCl and use the 1:2 mole ratio between CaCO₃ and HCl.

No. The same first coordinate may arise from different factor pairs with different sums. For example, \((a,b)=(0,0)\) gives the ordered pair \((0,0)\), while \((0,1)\) gives \((0,1)\). Thus input 0 has two images.

1. Odd natural numbers.
2. Even natural numbers.
3. Natural numbers not divisible by 3.
4. \(\{1\}\) together with all composite natural numbers.
5. Natural numbers not divisible by 15.
6. Natural numbers that are not perfect squares.
7. Natural numbers that are not perfect cubes.
8. \(\mathbb N-\{3\}\).
9. \(\mathbb N-\{2\}\).
10. \(\{1,2,3,4,5,6\}\).
11. Since \(2x+1>10\Rightarrow x>\frac{9}{2}\), the original set is \(\{5,6,\ldots\}\); its complement is \(\{1,2,3,4\}\).